Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
We plan to submit applications to 14,000-18,000 job postings. Table 1 in the attached analysis plan shows the required sample sizes for a range of minimum detectable effects sizes (MDES), assuming various baseline callback rates. Sample size calculations were conducted using the J-PAL Power Calculator with a significance level of 0.05 and power of 0.80. Our baseline callback rates come from previous similar audit studies (Darolia et al., 2014 and Deming et al., 2016) and from our own pilot study, where 21% of applicants received an interview request. We expect callback rates to be more in line with past literature (4-8%) than our pilot study, since the pilot focused on a tight labor market (early childhood education), but the full study will target industries similar to past literature. The estimates in Table 1 imply that even with the most conservative callback rate, we will be able to detect precise effects of 0.02 by submitting resumes to 17,400 job postings.
The estimates in Table 1 give sample size requirements to detect main effects. We are also interested in heterogeneous effects by field of study, race/ethnicity, gender, and labor market. The most conservative power analyses would multiply the sample sizes in Table 1 by the number of groups for each heterogeneity analysis: for example, assuming a callback rate of 0.08 and aiming for a MDES of 4 percentage points, we would apply to 1,634 job postings to detect main effects, but 1,926*3 = 5,778 job postings to detect heterogeneous effects across our 3 fields of study. Similarly, we would apply to 5,778 postings to detect heterogeneous effects by race/ethnicity, or 17,334 (1,926*3*3) postings to detect effects by race/ethnicity and field of study. Thus, our target number of 14,000-18,000 job postings will allow us to detect precise main effects under very conservative callback rates, as well as moderate effect sizes across multiple layers of heterogeneity under expected callback rates.